Question

A relation R on set {1,2,3,4,5} defined by the rule (x,y)∈ R if x+y≤6.
List the elements of R-1

Answer 1

Answer:⇒

• Suppose that you have two sets A = {1, 2} and B = {1, 2, 3}, and the relation is given by (x, y) ∈ R ↔ x − y is even.
• Since the relation is  a subset of A × B, we start by computing the cartesian product  
• A × B = {(1, 1),(1, 2),(1, 3),(2, 1),(2, 2),(2, 3)}.
• Then in this list of pairs, we select those which satisfy the relation R.
• For  example, for (1, 2), we have x = 1 and y = 2, we compute x−y = 1−2 = −1,
• which is odd, thus it does not belong to R.
• We try out similarly all the pairs  in A × B to get  R = {(1, 1),(1, 3),(2, 2)}.
• This may be visualized using a diagram:
• draw a circle to represent the set  A, and this circle contains two points, one for 1 and one for 2.
• Similarly,  draw a circle to represent B, and points of 1, 2, 3.
• Then an arrow from A to  B connects x in A with y in B if x − y is even.